Question

If three angles of a quadrilateral are ${70}^{\circ },{95}^{\circ }$ and ${105}^{\circ }$, then the fourth angle is :

• A. ${90}^{\circ }$
• B. ${100}^{\circ }$
• C. ${110}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

Answer: (A)

${90}^{\circ }$

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

The given angles are, ${70}^o,{95}^o,{105}^o$.

Let the fourth angle be $x^o$.

Then, ${70}^o+{95}^o+{105}^o+x^o={360}^o$.

$\Rightarrow$ ${360}^o-({70}^o+{95}^o+{105}^o)=x^{\circ }$

$\Rightarrow$ $x^o={360}^o-{270}^o={90}^{\circ }$.

Therefore, the fourth angle is $x^o={90}^o$.

Hence, option $A$ is correct.